powersystemfandomcom-20200214-history
Optimal Sizing of Battery Energy Storage System
Introduction to BESS Battery Energy Storage System (BESS) changes our life. Conventionally, power system is passive and hard to store electricity, so power between generation and demand must be balanced for 24/7. However, due to the advent of BESS, electricity can be stored and used afterward. Usually, there are three main important role of BESS. Peak-shaving The first role of BESS is peak shaving. Peak shaving is saving power in BESS when load-level is low (at off-peak time), and make the output when load-level is high (at peak time). Peak shaving helps owner of BESS to increase social welfare or make profits. Fig. 1 shows the peak shaving using BESS. Mitigating/maximizing the output of RESs Secondly, using BESS, the output of Renewable Energy Sources (RES) can be mitigated or maximized. Usually, the output of RESs, such as wind generator and PV generator, is fluctuating because it depends on wind speed, solar radiation, and etc. Fluctuations of the output have deteriorating effect on reliability of power system. When the output of RESs is fluctuating, the BESS can mitigate the fluctuation and improve the reliability. Most RESs are operating in Maximum Power Point Tracking (MPPT) mode to generate maximum power. But, sometimes RESs are operating for deloaded-mode which makes the output be lower than MPPT modes to improve the reliability of power system. However, if BESS is used, RESs can operate in MPPT mode because BESS can improve the reliability. Fig. 2 shows how BESS mitigates the output of RESs. Frequency Regulation The third one is frequency regulation. Primary frequency control and secondary frequency control need fast-response sources. Because BESS has feature of fast response, it is very effective to use BESS in primary/secondary control. Fig. 3 shows how BESS helps frequency regulation. Optimal size of BESS There are many researches related to operation and control using BESS. Also, a lot companies study and provide Battery Energy Management System(BEMS) solutions. When someone gets BESS, operation scheme and controller, or BEMS should be developed. However, before possession of operation scheme and controller or BEMS, location of BESS and size of BESS should be decided. Planning, such as location and sizing, is the first one to be considered. Benefits and social welfare can be increased by location of BESS and size of BESS, therefore, planning of BESS is important problem and it can be optimization problem. When optimal size of BESS is found, optimal size of BESS used for peak-shaving and mitigating/maximizing of the output of RESs can be obtained. However, the size of BESS used for frequency regulation can not be optimized because BESS is used for control which is not for optimization. In this paper, we just focus on the BESS used for peak-shaving and mitigating/maximizing of the output of RESs. Two types of Owner : Utility and Demand-side-BESS-owner Sizing of BESS should be decided toward maximizing benefits and social welfare. There are two types of owners. The first one is utility and the second one is demand-side-BESS-owner. Utility supervises whole power system and demand-side-BESS-owner supervises only their area. Utility and demand-side-BESS-owner(in Fig. 4, customer represents demand-side-BESS-owner) are shown in Fig. 4. Upper figure shows managed area of utility, and lower figure shows managed area of each demand-side-BESS-owner(Customer). They have different purpose for using BESS. The objective of utility is maximizing social welfare. However, the objective of demand-side-BESS-owner is maximizing their profits or benefits. Two types of optimization problem are handled below. A. The view of utility This section is dealing with BESS sizing in point of BESS owning utilities’ view. Utilities use BESS to make additional social welfare. BESS is used to shave peak load, mitigate the output from RES or provide ancillary services. (1) Optimal sizing of BESS to shave load peak In T.Lee and N. Chen, "Optimal capacity of the battery energy storage system in a power system," IEEE Trans. Energy Convers, vol. 8, no. 4, 1993. C. Lo and M. D. Anderson, "Economic dispatch and optimal sizing of battery energy storage systems in utility load-leveling operations," IEEE Trans. Energy Convers., vol. 14, no. 3, pp. 824-829, 1999., mixed-pass dynamic programming (MPDP) is used to find optimal size of BESS. Objective function for optimal size of BESS is presented as ratio of fuel cost saving over capital cost of BESS as 3.1.1.(1). max \frac{FS}{CPL}\cdots 3.1.1.(1) FS : Fuel cost savings due to BESS, CP : Capital cost of BESS CP = C_{E}E^{rated} +C_{S}S^{rated} \cdots 3.1.1.(2) C_{E} : cost of energy capacity related to amount of capacity, C_{S} : cost of rated power related to BESS, E^{rated} : energy capacity, S^{rated} : rated power Fuel cost saving is generated from peak shaving by using BESS. Capital cost of BESS consists of cost of power capacity (W) and cost of energy capacity (Wh). Power capacity cost is related to cost of power converter system, and cost energy capacity is related to sum of batteries, costs of infrastructures and facilities, and engineering costs. There are several papers W. Bingying, Z. Buhan, M. Biao, and Z. Jiajun, “Optimal capacity of flow battery and economic dispatch used in peak load shifting,” IEEE International Conference on Electric Utility Deregulation and Restructuring and Power Technologies, pp.1395-1400, 2011., M. Nick, M. Hohmman, R. Cherkaoui, and M. Paolone, "Optimal location and sizing of distributed storage systems in active distribution networks," in Proc. IEEE PowerTech, 2013, pp. 1–6. focusing on other purpose together with peak load shaving. Security constraints of voltage and frequency are considered in . Voltage support of BESS and network losses are considered in objective function of with BESS site and size as variables in . In M. Alhaider and L. Fan. "Mixed integer programming based battery sizing." Energy Systems Springer, 2014, pp. 787-805., BESS sizing problem is sectioned into two parts; utility’s point of view and consumer’s point of view. In the view of utility, objective function is formed as generation cost. Mixed integer programming model treating power/energy size as decision variable is used to find optimal size of BESS. Switchable loads are included, and the turning off penalty of switchable loads is given as average electricity rate. Power loss in power balance equation, spinning reserve requirements, unit minimum up/down time, and ramp constraint constraints are considered as constraints. Differing from , the author of S. Chakraborty, T. Senjyu, H. Toyama, A. Y. Saber, and T. Funabashi, "Determination methodology for optimising the energy storage size for power system." IET Generation, Transmission & Distribution, vol. 3, no. 11, pp. 987–999, 2009. integrates welfare of utility and community in one objective function. The objective function is established with increased savings due to use of BESS subtracted by costs. As savings by BESS, emission cost saving and distribution network savings are added to fuel cost saving. Distribution network saving include savings obtained from ancillary services providing reactive power and savings from peak shaving. Considering both fuel cost saving and saving of peak shaving is result of dealing whole society welfare. To reflect life-cycle cost of BESS, operating and maintenance costs respectively related to rated power and annual discharge energy variables are added to previously presented capital cost of BESS. Objective function is formulated as summation of savings subtracted by life-cycle cost of BESS. Size of BESS is calculated with heuristic-based approach that includes iterations dealing power/energy capacity as parameters. At first several power/energy parameters are generated, generators are scheduled, and revenue is calculated. There are two iteration loop; local iteration and global iteration (inner and outer loop). At the beginning of new iteration power/energy capacity pair is generated in neighborhood of existing pair. The revenue by the generated pair is compared with existing one and one of the pairs is chosen with larger revenue at the end of iteration. Because the solution is solved by heuristic method that use BESS capacity as parameters, the result is feasible but not always optimal. In F. A. Chacra, P. Bastard, G. Fleury, and R. Clavreul, "Impact of energy storage costs on economical performance in a distribution substation." IEEE Trans. Power Syst., vol. 20, no. 2, pp. 684–691, May 2005, savings are established further on the view of distribution network savings. Not only saving of peak shaving and ancillary service savings also upgrades deferral savings and reduction of annual invoice for utilization of power transmission network are included. As the amount of power flow becomes larger year by year, facilities of substation need to be reinforced. But if peak load is shaved with BESS, substation upgrade can be deferred and lead to saving cost which is the function of load consumption growth rate, peak load reduction ratio. In France, customers subscribe to power of demand and annual invoice is charged according to subscribed power. If customer overuse power more than subscribed, penalty charge is added. But this penalty can be avoided by using BESS. Cost is considered same as , life-cycle cost of BESS. To formulate net present value (NPV) as objective function, inflation and discount rate are considered. NPV is dissociated into three parts which are element of multi-objective function and solved by non-dominated sorting genetic algorithms (NSGA) using multiple objective technique. With vector composed of power of BESS at each hour, Pareto front is comprised of non dominated solutions. Using Preto front as candidate for optimal solution generic algorithm is conducted. (2) Optimal sizing of BESS which is used for mitigating/maximizing output of RES In Y. M. Atwa, E. F. El-Saadany, M. M. A. Salama, and R. Seethapathy, "Optimal renewable resources mix for distribution system energy loss minimization,” IEEE Trans. Power Syst., vol. 25, no. 1, pp. 360–370, Feb. 2010., the authors focus on the spilled wind energy. As mentioned before, RESs generate no maximum output because of reliability. Reduced wind energy for reliability is the spilled wind energy. The objective function is the cost of spilled wind energy. The spilled energy is related to the size of ESS and the rated power and energy capacity of BESS is decision variables. The purpose is to maximize the objective function. In other words, the way to maximize the spilled wind energy is the way to decide optimal size of BESS. In Q. Li, S. S. Choi, Y. Yuan, and D. L. Yao, “On the determination of battery energy storage capacity and short-term power dispatch of a wind farm,” IEEE Trans. Sustain. Energy, vol. 2, no. 2, pp. 148–158, Apr. 2011., the system consists of conventional generator, BESS, wind farm, and loads. BESS is used for mitigating output of wind farm. It means wind farm can generate the desired output and wind farm can be dispatched and can participate in electricity market due to BESS. Dispatch value of wind farm is decisions variables, and the size of BESS can be expressed by dispatch value. The objective function is . The purpose is to maximize the objective function. Life time cost and operating cost are function of the size of BESS. lifetime cost is estimated by the numerical approach. The optimal size of BESS is decided. B. The view of demand-side-BESS-owner In this section, we focus on the research related to the view of demand-side-BESS-owner. The objective of researches is maximizing owner’s profit. In the most researches, it is assumed that demand-side-BESS-owners have loads, ESS and DGs(sometimes, they have conventional generators). Demand-side-BESS-owner can be just customer or community which is a big customer, such as LSEs, or distribution network operators. The energy storage sizing problem related to Demand-side-BESS-owner has been frequently addressed in the literature ,,. (1) Optimal sizing of BESS which is used for peak shaving Especially, in ,,, Optimal size of BESS is found in order to maximize benefits of customers and community which have BESS and loads. In T. Y. Lee and N. Chen "Determination of optimal contract capacities and optimal sizes of battery energy storage systems for time-of-use rates industrial customers," IEEE Trans. Energy Convers., vol. 10, no. 3, pp. 562–568, Sep. 1995., authors assume that customers are Time Of Use(TOU) rates customer. TOU rates consist of three time period : Peak load hour, medium load hour, and light load hour. The objective is maximizing saved electricity cost considering the capital cost. Saved cost can be expressed by total electricity charge without BESS minus total electricity charge with BESS. Capital cost is comprised of battery cost, converter cost, balance of plant cost and maintenance cost. Therefore, the objective function is saved cost/capital cost and goal is to maximize the objective function. Capacity and rated power of BESS are closely related and they are the decisions variable. Through maximizing objective function, optimal capacity and rated power of BESS can be determined. AMPDP is used for optimizing method which is an improvement of multi pass dynamic programming(MPDP). In A. Oudalov, R. Cherkaoui and A. Beguin, "Sizing and Optimal Operation of Battery Energy Storage System for Peak Shaving Application,”IEEE Powertech Conf., pp. 621–625, July 2007. , authors approach similar way to , but they compose the objective function different way. The objective function is expressed by benefits minus capital cost and authors assume benefits are proportional to required maximum power to shave. Likewise, through maximizing objective function, optimal capacity and rated power of BESS can be determined. Dynamic Programming(DP) method is used for optimization. In , demand-side-BESS-owner is not just load customer. a little community has a BESS. Community has loads and BESS, and is connected with the main grid. The community owner can import power from the external main grid. There is contract between the external main grid and community. If power deviation from schedule value of import power occurs, community must pay the penalty. Hence, The objective function consists of the total cost which is the sum of the cost of imported power, the cost of the BESS and the penalty due to imported power deviation from the scheduled power. The main purpose is to minimize the objective function and power and energy rating of the BESS are decisions variables. Because the owner of BESS is not just customer, but community which is bigger than customer and is a system. For this reason, power balance, power rating limits of BESS, energy rating of BESS, and imported power limits should be considered and these are the constraints. Mixed integer programming(MIP) is used for optimization. In Y. Ru, J. Kleissl, S. Martinez, "Storage size determination for grid-connected photovoltaic systems," IEEE Trans. Sustain. Energy, 2013, demand-side-BESS-owner is a customer who has BESS, PV, and loads. In a different way to ,,, it contains RES. Time of use electricity pricing is used and customer sells electricity when the price is high and imports electricity when the price is low. The objective is to minimize the cost associated with purchasing from(or selling back) the electricity grid and the BESS capacity loss while at the same time satisfying the load and reducing the peak electricity purchase from the grid. For this reason, the objective function depends on the chosen battery size. (2) Optimal sizing of BESS which is used for mitigating/maximizing output of RES ] In S. W. Alnaser, L. F. Ochoa, "Optimal sizing and control of energy storage in wind power-rich distribution networks", IEEE Trans. Power Syst., Vol. 31, No. 3, May 2016, demand-side-BESS-owner is a Distribution Network Operator(DNO). The authors want to find optimal size of BESS for maximizing outputs of DGs. Because of fluctuation of RESs, there is reliability prbolem. For increasing reliability, DGs do not generate their full rated power although DGs can generate more power. For this reason, purpose is to maximize DGs output using BESS. Curtailment of DGs means full rated power minus actual generating power. Purpose can be minimize curtailment. The authors use OPF. At first, set the disired curtailment level. then, multi period AC OPF is performed. The objective function is to minimize capital cost of BESS. Constraints are about 1) storage facilities, 2) controllable DG Plants constraint, 3) On-Load Tap Changers, and 4) general AC OPF constraints. Optimal solution could be optimal energy size/rated power of ESS. Using the optimal size of BESS, find the optimal actual curtailment of DGs. Then, compare actual curtailment with desired curtailment which is set at first. If the difference is bigger than criteria, iteration repeats. Otherwise, optimal solution can be gotten. Fig. 5. is the algorithm of 14. 3.2.2.(1),3.2.2.(2) are the objective function of first stage and second stage. min \sum C_{E}E^{rated} +C_{S}S^{rated} \cdots 3.2.2.(1) max \sum p_{n} \cdots 3.2.2.(2) C_{E} : relative cost of energy capacity, C_{S} : relative cost of rated power, E^{rated} : energy capacity, S^{rated} : rated power, p_{n} : output power of DGs . .